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Theorems · Theorem · commutative algebra

Algebra.Smooth.comp

∀ (R : Type u_4) [inst : CommRing R] (A : Type u_5) (B : Type u_6) [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [inst_3 : CommRing B] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] [Algebra.Smooth R A]
  [Algebra.Smooth A B], Algebra.Smooth R B

Smooth is stable under composition.

Defined in
Mathlib.RingTheory.Smooth.Basic
Cited by
1 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.SmoothAlgebra.Smooth
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.Smooth.comp · cited by 1Smooth.compCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsScalarTower · cited by 3896IsScalarTowerAlgebra.Smooth · cited by 22Algebra.SmoothAlgebra.FormallySmooth.comp · cited by 9FormallySmooth.compAlgebra.FinitePresentation.trans · cited by 8FinitePresentation.transSmooth.compCITED BYCITES

Cites6

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Cited by1

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